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trigonometry
MUFF WIGGLER Forum Index -> Music Tech DIY  
Author trigonometry
AnalogFan
Hi there,

i need some help with "trigonometry"



i need find the metric coordinates of pin 1.
we know the angle and the hypotenuse, what to do next?

thnx in advance.
diode_destroyer
So with respect to the middle axes/coordinate system, pin 1 is to the right by 6.5sin(45deg) (calculator in deg mode!) = 6.5/sqrt(2) = 4.59619 and it is down by 6.5cos(45) = (also) 6.5/sqrt(2) = 4.59619. (In whatever units your original numbers are in, e.g. mm.)
AnalogFan
diode_destroyer wrote:
So with respect to the middle axes/coordinate system, pin 1 is to the right by 6.5sin(45deg) (calculator in deg mode!) = 6.5/sqrt(2) = 4.59619 and it is down by 6.5cos(45) = (also) 6.5/sqrt(2) = 4.59619. (In whatever units your original numbers are in, e.g. mm.)


indeed, thanx very much. awesome

i did research and your info is the same, but i stumbled on the squareroot.
ranix
here's a fun trick to avoid doing trigonometry. You can do it if the program you're designing your board in has a circle or arc tool, or if you are making a drawing on paper with a compass and a straightedge.



Be careful with this technique, you can accidentally discover the secrets of the universe.
JakoGreyshire
Funny thing about the universe secrets... hihi
Bodo1967
diode_destroyer wrote:
(In whatever units your original numbers are in, e.g. mm.)


That looks like a PCB template for a 1/4 inch jack - one of those:



So yes, mm should be the correct unit.
whoop_john
If what you are trying to do is place that pin in a PCB program, I usually deal with it by placing a temporary pin at the rotation point and group it with the pin I want to rotate, placed on one of the cardinal points. Then I can rotate the grouped pair by 45º by clicking on the temporary pin, ungroup and delete the temporary pin. It works for me, quicker to do than explain, but I use Osmond PCB on the Mac, so I don't know if other programs will do similar things.

You could probably eyes... it well enough by drawing a circle of the correct radius and a 45º line from the centre. Where they cross is your pin location.
butter
Can also do it with geometry and some algebra...

A 45degree segment is the diagonal of a square, so we know that the horizontal and vertical co-ordinates should be equal lengths (being 2 sides of a square).

So we have pythagoras':
h^2=x^2+y^2
but x=y here, so
h^2=2x^2
42.25=2x^2
21.125=x^2
x=4.59619407771
AnalogFan
diode_destroyer wrote:
So with respect to the middle axes/coordinate system, pin 1 is to the right by 6.5sin(45deg) (calculator in deg mode!) = 6.5/sqrt(2) = 4.59619 and it is down by 6.5cos(45) = (also) 6.5/sqrt(2) = 4.59619. (In whatever units your original numbers are in, e.g. mm.)



how to find the coordinates of A,B, i tried the same trick and deduce from X,Y (-4.59619), but that didn't work. i did read up on Pythagoras and the Cartesian, but i couldn't find the answer on how to find the second coordinates.



i need to have that line spot on the hole and as wide as specified on the drawing, 2.5 mm or 1.25 mm north west and 1.25 mm "south east"


thnx in advance.
AnalogFan
Bodo1967 wrote:
diode_destroyer wrote:
(In whatever units your original numbers are in, e.g. mm.)


That looks like a PCB template for a 1/4 inch jack - one of those:



So yes, mm should be the correct unit.


yes it is
razz
PJ612A 1/4 inch Jacks
AnalogFan
ranix wrote:
here's a fun trick to avoid doing trigonometry. You can do it if the program you're designing your board in has a circle or arc tool, or if you are making a drawing on paper with a compass and a straightedge.



Be careful with this technique, you can accidentally discover the secrets of the universe.


thnx, that's how i learned it at school, but the grid in eagle!
EATyourGUITAR
North south east and west are depreciated in 2 dimensional coordinate systems since they are intended to describe vectors on a spheroid earth in 3 dimensional space. Mathematicians now prefer up down left right or you can use degrees, radians, phase angle, vectors or anything else but not that. Dead Banana
AnalogFan
EATyourGUITAR wrote:
North south east and west are depreciated in 2 dimensional coordinate systems since they are intended to describe vectors on a spheroid earth in 3 dimensional space. Mathematicians now prefer up down left right or you can use degrees, radians, phase angle, vectors or anything else but not that. Dead Banana


thnx, but this type of Maths is rusty and that is what came up in me.
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